PoissonSGZ: Poisson Shifted Gompertz (PSG) Distribution

Description

Provides density, distribution, quantile, random generation, and hazard functions for the Poisson Shifted Gompertz distribution.

Usage

dpois.shifted.gz(x, alpha, beta, lambda, log = FALSE)
ppois.shifted.gz(q, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
qpois.shifted.gz(p, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
rpois.shifted.gz(n, alpha, beta, lambda)
hpois.shifted.gz(x, alpha, beta, lambda)

Value

dpois.shifted.gz: numeric vector of (log-)densities
ppois.shifted.gz: numeric vector of probabilities
qpois.shifted.gz: numeric vector of quantiles
rpois.shifted.gz: numeric vector of random variates
hpois.shifted.gz: numeric vector of hazard values

Arguments

x, q: numeric vector of quantiles (x, q)
alpha: positive numeric parameter
beta: positive numeric parameter
lambda: positive numeric parameter
log: logical; if TRUE, returns log-density
lower.tail: logical; if TRUE (default), probabilities are $P[X \le x]$ otherwise, $P[X > x]$.
log.p: logical; if TRUE, probabilities are given as log(p)
p: numeric vector of probabilities (0 < p < 1)
n: number of observations (integer > 0)

Details

The Poisson Shifted Gompertz distribution is parameterized by the parameters $\alpha > 0$, $\beta > 0$, and $\lambda > 0$.

The Poisson Shifted Gompertz distribution has CDF:

$$ F(x; \alpha, \beta, \lambda) = \quad \frac{1}{\left(1-e^{-\lambda}\right)}\left\{1-\exp \left[-\lambda\left\{1-\left(1-e^{-\beta x}\right) \exp \left(-\alpha e^{-\beta x}\right)\right\}\right]\right\}\quad ;\;x > 0. $$

where $\alpha$, $\beta$, and $\lambda$ are the parameters.

The following functions are included:

dpois.shifted.gz() — Density function
ppois.shifted.gz() — Distribution function
qpois.shifted.gz() — Quantile function
rpois.shifted.gz() — Random generation
hpois.shifted.gz() — Hazard function

References

Chaudhary,A.K., & Kumar, V. (2021). Poisson Shifted Gompertz Distribution: Properties and Applications. International Journal of Recent Technology and Engineering (IJRTE) ,9(5),202--208. tools:::Rd_expr_doi("10.35940/ijrte.E5265.019521")

Examples

Run this code

x <- seq(0.1, 10, 0.2)
dpois.shifted.gz(x, 2.0, 0.5, 0.2)
ppois.shifted.gz(x, 2.0, 0.5, 0.2)
qpois.shifted.gz(0.5, 2.0, 0.5, 0.2)
rpois.shifted.gz(10, 2.0, 0.5, 0.2)
hpois.shifted.gz(x, 2.0, 0.5, 0.2)

# Data
x <- fibers63  
# ML estimates
params = list(alpha=13.5877, beta=2.0139, lambda=18.8875)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = ppois.shifted.gz, fit.line=TRUE)

#Q-Q (quantile–quantile) plot 
qq.plot(x, params = params, qfun = qpois.shifted.gz, fit.line=TRUE)

# Goodness-of-Fit(GoF) and Model Diagnostics 
out <- gofic(x, params = params,
             dfun = dpois.shifted.gz, pfun=ppois.shifted.gz, plot=FALSE)
print.gofic(out)

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